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Question
Mr Sharma purchased a motorcycle for Rs 22,982.40 which included two successive discounts of 20% and 5% respectively on the basic price and then 8% sales tax on the remaining price. Find the basic price of the motorcycle.
Solution
Let the basic price be x
First rebate = 20 % of x
Cost of motorcycle after first discount = x - 20 % of x
`= "x" - (20 "x")/100`
`= (80 "x")/100`
Second rebate = 5 % of `(80 "x")/100`
Cost of motorcycle after seoond discount = `(80 "x")/100 - 5 % "of" (80 "x")/100`
`= (80 "x")/100 - (5/100 xx (80 "x")/100)`
`= (80 "x")/100 - (4 "x")/100`
`= (76 "x")/100`
Sales tax = 8 % of cost of motorcycle
`= 8/100 xx (76 "x")/100 `
`= (608 "x")/10000`
Total cost = cost + sales tax
`= (76 "x")/100 + (608 "x")/10000`
`= (8208 "x")/10000`
But total cost = Rs 22,982.40
⇒ `(8208 "x")/10000` = Rs 22982.40
⇒ x = `(22982.40 xx 10000)/8208`
⇒ x = Rs 28000
Hence, Basic price of motorcycle =Rs 28,000
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